Figure REF  depicts the trade-offs obtained by the competing approaches on the fairness tasks 1 and 2, on the Twitter dataset. Fig. REF  illustrates the superiority of GGF (green \(\square \) ) on Task 1, despite good performance of the baselines eq. utility (orange \(\times \) ) and welf (blue \(\circ \) ). As in one-sided recommendation with eq. exposure, the reason why eq. utility achieves slightly worse trade-offs on this fairness task is because it minimizes the std as a surrogate to the Gini index, instead of the Gini index itself as GGF does. For Task 2, on Fig.REF , we observe that GGF with parameterization (REF ) (green \(\square \) ) is the most effective. This is because unlike the welf approach (blue \(\circ \) ) of [1]} who address this fairness task, this form of GGF is exactly designed to optimize for utility quantiles.
